Date of Graduation


Document Type


Degree Type



Statler College of Engineering and Mineral Resources


Mechanical and Aerospace Engineering

Committee Chair

Wade W Huebsch

Committee Co-Chair

Patrick Browning

Committee Member

Christopher D Griffin


Though more obscure than traditional flight analysis, the tendency for a rigid body to flutter or tumble in flight during unstable conditions has been analyzed through physical experiments since the 1960s. In more recent years, similar conditions have been subjected to numerical simulation to further understand the effects of dimensionless properties on unstable body motion. It is important to understand dimensionless scaling relationships to compare properties of a body to that of a scaled model or for adjusting data when manufacturing limitations exist. For example, if the geometry of a scaled object could easily be manufactured, within tolerance, but material properties force the mass moment of inertia (MMOI) to deviate from an accepted value, dimensionless scaling relationships could aid in corrections for the desired MMOI. For tumbling bodies, two important properties are the angular velocity and the mass moment of inertia. However, the relationship between dimensionless MMOI and dimensionless angular velocity remains unclear. The purpose of this study was to understand how changing MMOI affects the behavior of angular rates for a rigid body, influenced by repeatable initial conditions and try to characterize that relationship. Using four blocks of varying size and MMOI, a series of tests were conducted to subject the blocks to a range of angular velocities between 0.3 radians/sec and 36.5 radians/sec. Body rates were difficult to measure using standard recording devices; therefore, two different high-speed camera systems were used to calculate body rates. Methods: Four different block sizes were manufactured to receive two additional masses. The additional masses were inserted symmetrically about the x, y, and z axes of the block. In order to change the MMOI of the block while also preserving its mass, geometry, and density, the additional masses were placed in one of three locations. The first of four different tests involved exposing the blocks to the same initial force at a location that produced rotation about the z axis. Supported uniformly by free jets of air, the blocks traveled horizontally across a flat table. A Photron SA5 was used to record a trajectory at 500 fps, and the software Tracker was used to evaluate rates. The second test evaluated body rates as the blocks fell from a height of 243 cm. For each randomized test, the MMOI of the block was changed by adjusting the location of additional masses. Again, using a Photron SA5, high speed video was taken at 500 frames per second (fps) during testing to analyze average linear and angular velocities in the software. The third and fourth tests involved an arm-spring mechanism (i.e. clay pigeon thrower) to induce translational and rotational velocity. However, the third test, just as the first and second, used the software Tracker to evaluate rates. In contrast, the fourth test involved a larger volume over which to track the block's trajectory, and a Vicon camera system was used to evaluate rates. From the high-speed data, a power law scaling relationship between dimensionless MMOI and dimensionless angular velocity was determined. However, the scaling relationship was limited to calculating a velocity ratio rather than individual velocities, due to the translational velocity and rotational velocity being dependent on one another. A two-factor Analysis of Variance (ANOVA) analysis on the data showed that geometric properties of the body greatly influenced the data when compared to the changing MMOI and interaction between the factors.